I've been trying to work this one through. One possible solution, (using a hefty dose of mathematical illiteracy, that looks like one of those word problems that occasionally appears in Marilyn vos Savant's column):

  base salary: $100
  $100 * 1.2 = $120
  $120 * (1.2 * .8) = $115.2

("It's a 20% pay cut from our pay raise, that's why you have to multiply our pay raise with our pay cut.")

Technically he didn't say that it was the pay that was being added and subtracted. Perhaps it could have been something like, say, hours?

If a sum of money (S0) is increased with p percent then decreased with the same percent, the final sum (S2) will be:

   S2 = S0 * (100+p)/100 * (100-p)/100

A plot[1] of this equation will quickly show that as p increases, S2 decreases.

[1] http://www.wolframalpha.com/input/?i=%28100%2Bp%29%2F100+*+%...

True. 20% of y is larger than 20% of x (which is what was added to x to obtain y) because y is a larger number. Therefore subtracting 20% of y from y will give you some value smaller than x. Eg: 100 + 20% = 120; 120 - 20% = 96.

Not that anyone here needs an explanation :)

I don't whether the error you introduced is intentional or not, but 120 * 0.8 = 96, not 106.

Another way of thinking about this is that 1.2 * 0.8 = 0.96, so it is a four percent pay cut. (This is true for any situation like this and can be remembered by the difference of two squares formula from your early algebra class -- (1 + r)(1-r) = 1 - r^2, where r is the fraction raise/pay cut.)

120 * 0.8 = 96, not 106

It would make sense if the amount in question was from a deduction from pay of some sort, tax, union fee deduction etc., rather than the pay itself.